Fast anti-aliased circle generation

This chapter discusses the fast anti-aliased circle generation. This gem proposes an elegant technique to render anti-aliased circles with even less number of operations than Bresenham's incremental circle algorithm. The success is credited to a simple two-point anti-aliasing scheme and the use of a table of size max, where √2/4 Rmax is the maximum circle radius allowed by the new algorithm. Due to the eight-way symmetry of the circle, it suffices to consider the circle x² + y² = r² in the first octant. It is found that to suppress the image jaggies caused by insufficient spatial sampling on a grayscale display, one may plot all pixels immediately to the right and left of the true circular arc with their intensities inversely proportional to their distances to the arc. It is found that to keep even intensity on the digital circle, it is assumed that the total intensity I of two horizontally adjacent pixels be a constant. It is supposed I(i, j) be the pixel value at the raster point (i, j) and then the linear intensity interpolation between the two adjacent pixels is given.